FYKOS Year 31 Series 6 Problem 3 — non-analytic spring · FYKOS 31 #31.6.3

Physics · mechanics

Problem

Imagine a pole of length

b = 5 \mathrm{cm}

and mass

m = 1 \mathrm{kg}

and a spring of initial length

c = 10 \mathrm{cm}

, spring constant

k = 200 \mathrm{N\cdot m^{-1}}

and negligible mass, that are connected at one of their ends. The other ends of the spring and the pole are affixed at the same height

a = 10 \mathrm{cm}

from each other. The spring and the pole can both freely rotate about the fixed points and their joint. Label

\phi

the angle of the pole to the horizontal. Find all angles

\phi

, for which the system is in an equilibrium. Which of these are stable and which unstable?